






"""simple docstring"""


def        UpperCAmelCase      (					a__     ,      a__ ):





						'''simple docstring'''






						_enforce_args(a__     ,      a__ )
						if n == 0:
												return 0
						lowerCAmelCase   :Any						=			float('-inf' )
						for i in range(1     ,      n + 1 ):
												lowerCAmelCase   :Dict						=			max(
												    a__     ,      prices[i - 1] + naive_cut_rod_recursive(n - i     ,      a__ ) )

						return max_revue


def        UpperCAmelCase      (					a__     ,      a__ ):





						'''simple docstring'''






						_enforce_args(a__     ,      a__ )
						lowerCAmelCase   :Dict						=			[float('-inf' ) for _ in range(n + 1 )]
						return _top_down_cut_rod_recursive(a__     ,      a__     ,      a__ )


def        UpperCAmelCase      (					a__     ,      a__     ,      a__ ):





						'''simple docstring'''






						if max_rev[n] >= 0:
												return max_rev[n]
						elif n == 0:
												return 0
						else:
												lowerCAmelCase   :Optional[int]						=			float('-inf' )
												for i in range(1     ,      n + 1 ):
																		lowerCAmelCase   :Any						=			max(
																		    a__     ,      prices[i - 1] + _top_down_cut_rod_recursive(n - i     ,      a__     ,      a__ )     ,      )

												lowerCAmelCase   :Dict						=			max_revenue

						return max_rev[n]


def        UpperCAmelCase      (					a__     ,      a__ ):





						'''simple docstring'''






						_enforce_args(a__     ,      a__ )

						# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
						# length 0.
						lowerCAmelCase   :Optional[Any]						=			[float('-inf' ) for _ in range(n + 1 )]
						lowerCAmelCase   :List[Any]						=			0

						for i in range(1     ,      n + 1 ):
												lowerCAmelCase   :List[str]						=			max_rev[i]
												for j in range(1     ,      i + 1 ):
																		lowerCAmelCase   :List[Any]						=			max(a__     ,      prices[j - 1] + max_rev[i - j] )

												lowerCAmelCase   :List[str]						=			max_revenue_i

						return max_rev[n]


def        UpperCAmelCase      (					a__     ,      a__ ):





						'''simple docstring'''






						if n < 0:
												lowerCAmelCase   :Optional[int]						=			F"""n must be greater than or equal to 0. Got n = {n}"""
												raise ValueError(a__ )

						if n > len(a__ ):
												lowerCAmelCase   :Tuple						=			(
												    'Each integral piece of rod must have a corresponding price. '
												    F"""Got n = {n} but length of prices = {len(a__ )}"""
												)
												raise ValueError(a__ )


def        UpperCAmelCase      (					):





						'''simple docstring'''






						lowerCAmelCase   :List[str]						=			[6, 10, 12, 15, 20, 23]
						lowerCAmelCase   :Optional[Any]						=			len(a__ )

						# the best revenue comes from cutting the rod into 6 pieces, each
						# of length 1 resulting in a revenue of 6 * 6 = 36.
						lowerCAmelCase   :Union[str, Any]						=			36

						lowerCAmelCase   :Any						=			top_down_cut_rod(a__     ,      a__ )
						lowerCAmelCase   :int						=			bottom_up_cut_rod(a__     ,      a__ )
						lowerCAmelCase   :Optional[Any]						=			naive_cut_rod_recursive(a__     ,      a__ )

						assert expected_max_revenue == max_rev_top_down
						assert max_rev_top_down == max_rev_bottom_up
						assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
		main()







"""simple docstring"""


from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass




@dataclass
class 						__UpperCamelCase     :
					lowercase_    :				int
					lowercase_    :				TreeNode | None      =  None
					lowercase_    :				TreeNode | None      =  None


__SCREAMING_SNAKE_CASE   =   namedtuple('CoinsDistribResult', 'moves excess')


def        UpperCAmelCase      (					a__ ):





						'''simple docstring'''






						if root is None:
												return 0

						# Validation
						def count_nodes(a__ ) -> int:
												if node is None:
																		return 0

												return count_nodes(node.left ) + count_nodes(node.right ) + 1

						def count_coins(a__ ) -> int:
												if node is None:
																		return 0

												return count_coins(node.left ) + count_coins(node.right ) + node.data

						if count_nodes(a__ ) != count_coins(a__ ):
												raise ValueError('The nodes number should be same as the number of coins' )

						# Main calculation
						def get_distrib(a__ ) -> CoinsDistribResult:

												if node is None:
																		return CoinsDistribResult(0     ,      1 )

												lowerCAmelCase	, lowerCAmelCase   :Optional[int]						=			get_distrib(node.left )
												lowerCAmelCase	, lowerCAmelCase   :str						=			get_distrib(node.right )

												lowerCAmelCase   :str						=			1 - left_distrib_excess
												lowerCAmelCase   :Optional[Any]						=			1 - right_distrib_excess

												lowerCAmelCase   :Any						=			(
												    left_distrib_moves
												    + right_distrib_moves
												    + abs(a__ )
												    + abs(a__ )
												)
												lowerCAmelCase   :Tuple						=			node.data - coins_to_left - coins_to_right

												return CoinsDistribResult(a__     ,      a__ )

						return get_distrib(a__ )[0]


if __name__ == "__main__":
		import doctest

		doctest.testmod()